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Über dieses Buch

I. The Topic and the structure of the Proceedings The papers in this book are the proceedings of a conference held at the Economics Department of the Graduate Faculty of the New School for Social Research in March 1985 in New York for which financial support was provided by .the West German Consulate. The topic of the conference was "Competition, Instability, and Nonlinear Cycles." A number of mathematical economists from Italy, West Germany, France, Japan, and the u.s. were invited as participants in this meeting. The conference was preceded by two other conferences in which several of the invited scholars had taken part. One, on "la gravitation des prix," took place in Nanterre, France,in March 1984. The other was held at the New School for Social Research in April 1984 on "Price of Production in Joint Production systems." Both conference were concerned with classical prices of production systems and their revival in the form developed by Sraffa and Pasinetti (1977). In these conferences, considerable interest arose in more properly modeling the dynamics of prices of production systems in a multi­ sectoral framework by utilizing modern mathematical tools of dynamical systems. Such a discussion on the dynamics of the classical process of competition and the stability of classical production prices was originally initiated by several papers by Nikaido (1977, 1983, 1984) and further pursued by several scholars (see Steedman, 1983; Boggio, 1980; Kuroki, 1983; Dumenil/Levy, 1983; Krause, 1983, 1984; Hosoda, 1985; Filippini, 1985).

Inhaltsverzeichnis

Frontmatter

On Modeling the Cross-Dual Dynamics of Competition

The Dynamic Equalization of Profit Rates for Input-Output Models with Fixed Capital

Abstract
Recently there have been numerous new interpretations of the classical competitive process (Hollander, 1973; Garegnani, 1983; Roncaglia, 1978; Shaikh, 1980; Semmler, 1984). There have also been several attempts to model classical competitive dynamics. Within the latter group two trends are emerging. One line of thought explores the dynamics of the competitive process on the basis of classical theory by referring to supply and demand analysis (Nikaido, 1977, 1983; Flaschel, 1983; Flaschel/Semmler, 1985a, 1985b; Duménil/Lévy, 1983, 1984; Franke, 1985; Boggio, 1984; Steedman, 1984). The other direction utilizes the theory of markup pricing to elaborate on the stability properties of classically oriented production price systems (Nikaido/Kobayashi, 1978; Krause, 1983; Fujimoto/Krause, 1985; Boggio, 1985; Catz/Laganier, 1984).
Peter Flaschel, Willi Semmler

The Equalization of the Rate of Profit Reconsidered

Abstract
It is well-known that Adam Smith distinguished between “the market price” and “the natural price”, and considered the latter as the central price to which the former tends to converge with the passage of time1). The concept of “the normal rate of profit (or the general rate of profit)” that is equal among all sectors and industries, which is common to David Ricardo, Karl Marx, and other Classical Schools, is also closely related to the concept of the central price.
Ryuzo Kuroki

A Cross-Over Gravitation Process in Prices and Inventories

Abstract
The point of departure of the present paper is a Sraffian system of production prices, with respect to a given real wage rate. These prices are interpreted as long-run equilibrium prices, i.e., they are not only bringing about a uniform rate of profit, but at the same time they are supposed to match underlying demands and supplies of commodities. We are concerned with modelling what happens outside a long-run equilibrium and with investigating the classical problem whether, or under what circumstances, the market prices obtained will tend to the given production prices. In order to make an analytical treatment possible, we shall employ, as so many others have, a two-sector framework. Moreover, all analysis will be done in continuous time. It will be seen that, in the model specified, we have to be prepared for the phenomenon of non-convergence. In a second step, it will be studied what conditions exclude a complete divergence of trajectories. Referring to relative magnitudes, this will finally allow us to apply the famous Poincaré-Bendixson Theorem and to establish the existence of limit cycles or closed orbits. If the long-run position is unstable, they are non-degenerate and stable (or at least partly so), where relative prices and relative quantities oscillate in a more or less regular manner around their equilibrium values.
Reiner Franke

Stability of Production Prices in a Model of General Interdependence

Abstract
In the modern theory of production prices — which is mainly derived from the works of Sraffa, Von Neumann and Leontief — the question of the relation between such prices and those actually prevailing in the economy has been for a long time almost completly neglected.
Luciano Boggio

Ergodic Price Setting with Technical Progress

Abstract
By Boggio [1], Dan et al. [2], Duménil/Lévy [4] and Krause [9], various dynamic processes of price setting have been designed which converge to prices of production. Thereby it was assumed for the production technology to remain constant over time. In this paper we demonstrate a convergence result also when technical progress is admitted, provided the latter does not end up with the land of Cockaigne of zero costs. (Section 4.) In addition, instead of assuming an exogeneously given real wage for workers (as is assumed in [1],[2],[4]) we allow consumption bundles to depend on prices. Our analysis is confined to circulating capital only. (Fixed capital is treated in [1].) The main tool in obtaining the result is an ergodicity property for inhomogeneous products of nonlinear positive operators. (Section 3.) For the latter we present a proof on the basis of some earlier results obtained by the authors ([5],[6],[8]).
Takao Fujimoto, Ulrich Krause

Microfoundations of Macrodynamics and Limit Cycles

Swinging along the Autostrada

Abstract
The greatest mistake in my career occurred when Schumpeter came to me in 1938 or ’39 and asked me to report on a very important new publication: the von Neumann paper given at the Monger seminar, a repetition of the one he had given in Princeton in 1932. When I got as far as realizing that he was including all remaining plant and equipment in annual output, I rashly judged it to be totally unrealistic, and I still do, though in retrospect I realize the immense simplifying power of the method. In any case, I, alas, reported back to Schumpeter that it was no more than a piece of mathematical ingenuity, failing to see that it contained two aspects close to Schumpeter’s heart — a rigorous solution to Walras’s central problem and a demonstration that the rate of profit arose from growth not quantity of capital. When I came to edit his papers for the final section of his History, I found no reference to what now appears to me to be one of the great, seminal works of this century, the omission being possibly the result of my own blindness. The beautifully spare architecture of its encompassing structure leaves one awestruck. Apparently without antecedents, it sprang full blown from that fertile brain. Demonstrating the existence of a solution to the economic problem wherein all goods could be produced at the lowest price and the greatest possible quantity, with price equal to cost and supply equal to demand for all goods, along with showing the necessity for maximal growth if dynamic equilibrium is to exist. So grandiose an achievement was, of course, achieved at a cost. My purpose here is to suggest how one may, with a modest reformulation, bring it closer to reality, without damaging its essentially robust and clarifying solutions. The von Neumann theory may appropriately be considered the progenitor of contemporary growth theory since it demonstrated that a decentralized, capitalist economy had to grow at a determinate, constant rate to clear its markets. Profoundly true though in some sense it is, this type of theory is painfully unrealistic for the turbulent history of industrial capitalism. Not only that but it contains two quite unacceptable assumptions: there is no technical progress and there is a constant real wage. The maximal growth rate depends vitally on the real wage, but the wage is exogenous instead of being determined by the functioning of the system. My proposal is that the economy first overshoots and then undershoots the von Neumann solution, but that, on the average over a longer period, achieves an analogous solution to his, thus leaving the essential result undamaged.
Richard M. Goodwin

Stability and Instability in a Dynamic Model of Capitalist Production (abridged version)

Abstract
What follows is part of a broader study concerning the properties of capitalist economies with regard to stability. These properties are analyzed on the basis of a microeconomic model of the competitive process, based on the classical principles derived from the works of Smith, Ricardo and Marx.1 From these classical microeconomic foundations, a classical macro analysis is established.
G. Duménil, D. Lévy

On a Microdynamics of a Nonlinear Macrocycle Model

Abstract
This paper attempts to base a macrodynamic cycle model on a classically oriented microdynamics. Classically oriented microdynamic models, as discussed in this book, are concerned with the stability of relative prices and outputs over time. Such models are, for example, developed in Nikaido (1983), Boggio (1984), Franke (1984), Dumenil/Levy (1984), Flaschel/Semmler (1985a, 1986), and Goodwin (1985). Cycle models, on the other hand, examine the stability of aggregates such as investment, outputs, and employment (see Kaldor, 1940; Goodwin, 1948, 1951, 1972; Hicks, 1950; Duesenberry, 1958; Klein/Preston, 1969; Chang/Smyth, 1971; Kalecki, 1971; Dana/Malgrange, 1981).
Willi Semmler

Stabilization Policy in a Nonlinear Business Cycle Model

Abstract
The notion that the capitalist economy is inherently unstable at the macroeconomic level has immediate plausibility in view of the long history of instability in capital accumulation. It has not become the dominant view among economists, however, perhaps because of the argument that the motions of real capitalist economies around their long run average growth paths are bounded, and because of the implicit assumption that an unstable motion cannot remain bounded. This implicit assumption is true for linear systems, because the motion of a linear system far from its equilibrium point is the same as its motion near its equilibrium, but not true for non-linear systems (as Blatt, 1983, argues). Nonlinear systems that are unstable around their equilibrium points can exhibit other forms of stability, particularly the form of the stable limit cycle to which the system returns whatever its starting point. This observation is intriguing in view of the tradition of viewing the motions of the capitalist economy around its long run growth paths as a cycle.
Duncan K. Foley

Linear and Nonlinear Macrodynamics

Some Extensions of a Classical Growth Cycle Model

Abstract
The famous Marxian law of capitalist accumulation has never been a theme of major interest in economic theory. This is not only due to the persistent fascination exerted by other parts of Marxian theory, e.g. the labour theory of value or the reproduction schemes. To a large extent, the situation seems to be a natural outcome of a predominant interpretation of the law in terms of the concentration and centralization of capital and the tendency of rising immiserization of labour in particular.
Jörg Glombowski, Michael Krüger

Growth Cycles in a Classical-Keynesian Model

Abstract
The analysis of capitalist economic dynamics is not a simple matter. Capitalist economies produce growth, business cycles, and from time to time major crises which threaten their very existence. Any attempt to examine the logic of these dynamics has to be forgiven for making simplifying assumptions and conveniently neglecting part of the story. What is striking about much of contemporary dynamic theory, however, is its great difficulty in providing convincing explanations of the conjunction of growth and cycle. In the basic multiplier-accelerator model, as Pasinetti (1974, pp. 54–82) has clearly shown, growth and cycles are mutually exclusive alternatives. To have both, some exogenous factor must intervene. The same is true for “Keynesian” econometric models, the solutions to which produce cycles only if hit by random shocks. The currently fashionable “equilibrium” business cycle theory of the Lucas (1975) variety is also subject to this embarrassment, since it derives cycles from the accelerator mechanism, but has nothing to say about growth.
Marc Jarsulic

Problems Concerning the Dynamic Analysis of a Keynesian Model with Perfect Foresight

Abstract
In his chapter V on the dynamic analysis of a Keynesian model Sargent (1979) analyzes the effects of a sudden change in the money supply (via open-market operations) for the case of adaptive expectations as well as for perfect foresight. However, the result he derives for the latter case (strict neutrality if the change in monetary policy is not foreseen and reaction which even precedes action when it is foreseen) look very odd when considered from the viewpoint of the standard dynamic analysis that he applies in the adaptive expectations case. Hence, solution methods must be different when the dynamic laws which govern prices and related expectations are changed from the adaptive to the perfect foresight case — despite the fact that only ordinary differential equations are applied in both cases. This change in methods and results is insufficiently explained and motivated by Sargent. Furthermore, and more importantly, his way of reasoning conceals significant ambiguities and inconsistencies in the analyzed dynamic situation.
P. Flaschel, R. Picard

Cyclical Growth: The Interdependent Dynamics of Industry and Agriculture

Abstract
Accumulation is one side of the golden coin of capitalism; the creation of the proletariat is the other. Historically, accumulation has meant the simultaneous dispossession of people and concentration of property, so that the dispossessed face the propertied in the free labor market (see Marx, I, pp. 614, 620, 624).
Edward J. Nell

Econometrics of the Dynamics of Proportions and Nonlinear Macrodynamics

The Stability of the Reproduction Scheme: Theoretical Discussion and Empirical Evidence for the United States, 1948–1980

Abstract
The schemes of reproduction presented by Marx in Volume II of Capital are generally held to be the ancestors of more modern linear models of production and growth. By their very simplicity the schemes of reproduction allow for a basic discussion of the problems of this type of model.
Michel Juillard

Testing Non-Linearity in Business Cycles

Abstract
Compared to studies that use linear models there are, relatively speaking, few attempts to test non-linear business cycle models. The existing work can be grouped under three broad categories. First, there is the class of structural models that have several non-linear properties, but end up generating (simulated) cycles with linear characteristics. [e.g. Hickman (1972)]. Second, there is some work on the estimation of non-linear time series models which characterize non-linear aspects of cyclical phenomena better. [e.g. Marraval (1983)]. Finally, a small number of papers have attempted to investigate non-linear cyclical behavior using non-regression based techniques. [e.g. Neftci (1984), DeLong and Summers (1984)]. This paper is a review of these approaches.
Salih N. Neftci

Backmatter

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